X3661

1st KIRIKAMI-MOSES POINT

X3661 and X3662 were considered by Seiichi Kirikami and Peter Moses in December, 2011, in connection with combos.
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 1, 2 }: Nagel Line { 75, 141 }: Central Line L(75, 141) { 6, 319 }: Central Line L(6, 319) { 76, 321 }: Central Line L(76, 321) { 257, 312 }: Central Line L(257, 312) { 297, 318 }: Central Line L(297, 318) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_319 = ISOTOMIC CONJUGATE OF X(79) (0.4549, 0.1161) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_297 = -HIRST INVERSE OF X(4) (0.8440, 1.0022) X_318 = ISOTOMIC CONJUGATE OF X(77) (0.5514, 0.2839) X_3661 = 1st KIRIKAMI-MOSES POINT (0.5037, 0.1669) A B C X1 X2 X75 X141 X6 X319 X76 X321 X257 X312 X297 X318 X3661 (a, b, c) = (5, 6, 7) | AB = 1

X3661 (1st KIRIKAMI-MOSES POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc(b^{2} + c^{2} + bc)\)
Barycentrics: \(b^{2} + c^{2} + bc : c^{2} + a^{2} + ca : a^{2} + b^{2} + ab\)
Search Value (6, 9, 13): \(3.526108453752\)
▸ Linear Combinations3 combinations

  • X3661 = \(3(a^{2} + b^{2} + c^{2})\) X2 + \((a + b + c)^{2}\) X8

  • X3661 = \((a + b + c)^{2}\) X1 - \(3(a^{2} + b^{2} + c^{2} + bc + ca + ab)\) X2

  • X3661 = \((bc + ca + ab)\) X75 + \(2(a^{2} + b^{2} + c^{2})\) X141

▸ Incident Central Lines18 lines

{1, 2}, {6, 319}, {7, 3620}, {9, 1654}, {63, 2896}, {69, 894}, {75, 141}, {76, 321}, {100, 761}, {192, 2321}, {226, 3212}, {257, 312}, {297, 318}, {320, 599}, {344, 966}, {469, 1829}, {1726, 3219}, {2082, 3305}

▸ Functional Relations7 relations